Do Uniforms Make a Difference in Speed Skating?

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Do Uniforms Make a Difference in Speed Skating?

Shani Davis of the U.S. skates in the prototype of the official US Speedskating suit.

Image: Pavel Golovkin/AP

It seems the USA speed skaters aren't doing as well as they had hoped to in the 2014 Winter Olympics. One idea is that the new uniforms could be part of the problem. I don't know much about skating, so I'm just going to do a rough estimation of the effect a uniform could have on speed skating. Remember, I said I don't know much about skating and this is just an estimate - you know, for fun.

Constant Power Humans
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Let me start with a simple model of a speed skater traveling at a constant speed. In this model, I will assume the following:

During a race, a human skater has a constant power output of some value P.

There is an air resistance force on the skater that is proportional to the velocity squared. The air resistance force is also proportional to the density of the air and some drag coefficient.

The drag coefficient depends on both the shape of the skater and the surface properties of the suit.

What does the human use all this power for? Two things. First, is moving arms and legs and stuff like that. The second is to work against the air resistance. I will call the fraction of power that goes towards the air resistance f.

Let's say that I have a skater with a power fP (so this is just the power fighting the air drag - but I will just call it *P *from now on) moving at a constant speed of v and all of this power is going into fighting the air resistance (which totally isn't true - but this should still work out ok). Now let's say the skater moves a distance s over some time interval. I can calculate the work and the power of the air resistance force and set that equal to the power of the human skater.

Now for some values. Let's look at the Men's 1500 meter race. The Olympic Gold medal went to Zbigniew Brodka from Poland with a time of 1:45.006 or 105.006 seconds. This would give him an average speed of 14.285 m/s. Now I just need an estimate for the human power. In this previous post on bikes going up hills, I used a power of 300 watts. I am going to bump that up to 350 watts because - you know, it's the Olympics and these guys are giving it EVERYTHING THEY GOT. If I just totally guess a air drag fraction of 0.25, this would put the air drag power at 87.5 Watts. With this, I can get an estimate for all the non-velocity stuff in the previous equation (the product of the density, cross sectional area, and drag coefficient). Maybe I could just call all of this stuff "K" (oh, might as well throw the 1/2 in there too).

I can solve for this K value for the top Olympic performer and I get 0.030017 kg/m. Ok, here is the fun part. Suppose that I increase this air drag stuff by just a super small amount. What effect would that have on the total time? Again, a reminder that I am making some assumptions here that aren't absolutely valid but will still give me an estimate of the effect of these things.

Here is a plot of the race times for a human with constant power but an increase in drag stuff. I have included points with the times of top 10 skaters (with calculated a values).

What does this say? It says that if all of these skaters were identical except for air drag, there would be about a 3 percent increase in drag from the first place skater to the 10th place. From this estimation, drag could be a significant factor in the race. The key words here are "could be". This is just an estimate that ignores many things.

Constant Drag Coefficient Humans
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What if I pretend like all the humans have the same body shape and uniforms so that they have the same drag coefficient? What if the only difference in race times is due to differences in human power output? Here is a plot of the race time as a function of a percent of the 87.5 watt power that fights the air.

From this function, it seems like a human with power of around 85.14 watts instead of 87.5 would be able to account for the a 1 second longer race. What does this mean? This means that differences in human power could also easily account for differences in time.

Is this crazy to even approach a problem this way? No. These assumptions are a type of spherical cow (here is the spherical cow reference for non-physicists). Even if the assumptions are totally crazy, they at least give us a place to start. From this, it seems reasonable to further explore the role of air drag in speed skating (which surely someone has already done).

What would be the next step? I would get a speed skater and start making changes to things (like power and uniform) and see what kind of times that produces. Yes, it isn't so simple to change things when dealing with humans, but it's a human sport.